Pakistani President Pervez Musharraf has said he hopes recent peace moves with India will lead to direct dialogue between the two countries.
Mr Vajpayee plans to visit Pakistan next year
His remarks, to former US President Bill Clinton, came after India's prime minister said he hoped to meet his Pakistani counterpart in January.
The latest overtures follow the surprise announcement by both sides of a ceasefire in Kashmir on Tuesday.
The Pakistani and Indian leaders last held direct talks in July, 2001.
In a statement, the Pakistani Government said General Musharraf had briefed Mr Clinton over the phone on developments in Pakistani-Indian relations.
Mr Musharraf had earlier told a visiting US Congressional delegation - including Mr Clinton's wife, Hillary - that recent events "must lead to a composite dialogue" to try to settle all outstanding issues between India and Pakistan, the statement said.
Pakistan has invited Indian Prime Minister Atal Behari Vajpayee to a regional summit taking place in Islamabad next year.
Mr Vajpayee told reporters in the Indian town of Lucknow the programme for his visit was being finalised.
Asked whether he would meet the Pakistani Prime Minister, Mir Zafarullah Jamali, Mr Vajpayee said he would be "very pleased if there is a meeting".
Kashmir has been the source of two India-Pakistan wars
Islamabad is hosting the Saarc summit of south Asian countries in January, and Pakistani officials have made no secret of their wish to see Mr Vajpayee take part.
While the summit will focus on issues such as trade and commerce, there will be an opportunity for Indian and Pakistani politicians to meet on the sidelines to discuss more contentious issues - such as Kashmir.
Both India and Pakistan control a portion of the old Himalayan kingdom of Kashmir, and both say they have a right to the whole.
Two of their three wars since independence have been fought over the divided territory.
Tit-for-tat artillery attacks across the informal border, or Line of Control (LoC), have been a daily fact of life for many Kashmiris.
Tuesday's ceasefire along the rugged LoC marks the first time in 14 years that Indian and Pakistani guns have fallen silent.
The truce came about after India accepted a unilateral Pakistani ceasefire offer, made on Sunday.
However, India has cautioned that the ceasefire remains fragile, until Pakistan can rein in the militants fighting against its rule in Kashmir.
Pakistan has denied fuelling a 14-year uprising in the state, which has left tens of thousands dead.